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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 45, Iss. 7 — Jul. 1, 1955
  • pp: 497–499

Resolving Power and Information

G. TORALDO DI FRANCIA  »View Author Affiliations

JOSA, Vol. 45, Issue 7, pp. 497-499 (1955)

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The degrees of freedom of an image formed by any real instrument are only a finite number, while those those of the object are an infinite number. Several different objects may correspond to the same image.

It is shown that in the case of coherent illumination a large class of objects corresponding to a given image can be found very easily. Two-point resolution is impossible unless the observer has a priori an infinite amount of information about the object.

G. TORALDO DI FRANCIA, "Resolving Power and Information," J. Opt. Soc. Am. 45, 497-499 (1955)

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  1. See, for example, R. K. Luneberg, Mathematical Theory of Optics (Brown University Press,.Providence, 1944),p. 390.
  2. S. A. Schelkunoff, Bell System Tech. J. 22, 80 (1943).
  3. C. J. Bouwkamp and N. G. De Bruijn, Philips Research Repts. 1, 135 (1946).
  4. G. Toraldo di Francia, Nuovo cimento, Suppl. 9, 426 (1952).
  5. A. Maréchal and P. Lacomme, Compt. rend. 234, 1865 (1952).
  6. G. Toraldo di Francia, Atti fond azione. "Giorgio Ronchi" 6, 73 (1951); 8, 203 (1953).
  7. G. W. King and A. G. Emslie, J. Opt. Soc. Am. 41, 405 (1951); 43, 658, 664 (1953).
  8. A. Blanc-Lapierre, Ann. inst. Henri Poincaré 13, 245 (1953). For further literature the reader may be referred to this paper.
  9. G. Toraldo di Francia, Optica Acta (to be published.)
  10. C. E. Shannon, Bell Telephone System Monograph B-1598 (1948), p. 51.
  11. Both of them can be revealed by phase contrast techniques.
  12. If only bright points were considered, the sample values would not be different from those of a uniformly bright image. No resolution would be possible.
  13. P. M. Woodward, Probability and Information Theory (Pergamon Press, London, 1953), p. 33.
  14. S. Goldman, Information Teory (Prentice-Hall, Inc., New York, 1954), p. 69.
  15. D. A. Bell, Information Theory (Pittman and Sons, London, 1953), p. 43.

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